Spatial evolution of nonlinear deep-water wave groups is studied experimentally and numerically. Spatial two-dimensional version of the Zakharov equation describing evolution of deep-water gravity waves is used to derive two 4th order evolution equations, for the amplitudes of the surface elevation and of the velocity potential. The scaled form of the equations is presented. The experimental results for wave groups with initial narrow spectrum are compared with the computations based on the unidirectional Zakharov equation and the Dysthe model. The very good agreement between the computational results based on both models with the experiments prompted an attempt to perform simulations for a wider initial spectral width, that formally violate the assumptions adopted in the derivation of the Dysthe model. The accuracy of the results based on the Dysthe model is checked against the solutions of the Zakharov equation, which is free of restrictions on the spectral width. Conclusions regarding the domain of validity of the Dysthe model are drawn.